Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x³ + 3x² y − y³ − 15x.

a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square).

b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the square.

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milcah answered 2 years ago

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and...

Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and (3,3) are stationary points of f and classify these points as maximum, minimum or saddle point. Obtain the maximum or minimum value of f.

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to...

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to calculate the critical points and all local minima, local maxima and saddle points. How should this be done?

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and...

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and fye(x, y). b) Find all critical points of f(x, y). c) Classify the critical points of f(x, y) (as local max, local min, saddle). 2.Consider f(x) = 2x-x2and g(x) = x2 a) [2 points] Find the intersection points (if any) of the graphs of f(x) and g(x). b) [4 points] Graph the functions f(x) and g(x), and shade the region bounded by: f(x), g(x),...

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Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find...

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find the intervals where f is increasing, and decreasing. (b) Find the intervals where f is concave up, and concave down. (c) Find the local maxima, the local minima, and the inflection points. (d) Find the Maximum and Minimum Absolute of f over [−2, 2].

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Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

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